Econ1150 - PS3
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Econ1150 - PS3
Due: Wednesday, March 15, 10:30AM
1. The cost of attending your university has gone up once again. Although you have been told that education is investment in human capital and carries a return of roughly 10% a year, you (and your parents) are not pleased. An administrators at your school argues that you are paying more for your education because the reputation of your institution is better than that of others. To investigate this hypothesis, you collect data on a random sample of 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report annual ranking. Next you perform the following regression
c一ost
R2
= 
,(
= 0.72 SER = 3, 773.35
where Cost is Tuition, Fees, Room and Board in dollars, Reputation is the index used in U.S. News and World Report (based on a survey of university presidents and chief academic officers), which ranges from 1 (“marginal”) to 5 (“distinguished”), Size is the number of undergraduate students, and Dpriv , Dlibart, and Dreligion are binary variables indicating whether the institution is private, a liberal arts college, and has a religious affiliation. The numbers in parentheses are heteroskedasticity-robust standard errors.
(a) Interpret the results and determine whether or not the coefficients are significantly different from zero. Do the coefficients have the expected sign?
(b) What is the forecasted cost for a liberal arts college, which has no religious affiliation, a size of 1,500 students and a reputation level of 4.5? (All liberal arts colleges are private.)
(c) Suppose that you switch from a private university to a public university, which has a ranking that’s 0.5 lower and 10,000 more students. What is the effect on your cost?
(d) What is the p-value for the null hypothesis that the coefficient on Size is equal to zero? Based on this, should you eliminate the variable from the regression? Why or why not?
(e) You want to test simultaneously the hypotheses that βsize = 0 and βdilibart = 0. Your regression package returns an F-statistic of 1.23. Can you reject the null hypothesis?
(f) Eliminating the Size and Dlibart variables from your regression, the estimated regression becomes
c一ost = 
,(
Reputation + 1
Dpriv 
,
Dreligion
R2 = 0.72, SER = 3, 792.68
Why do you think that the effect of attending a private institution has increased now?
(g) You make one final attempt to bring the effect of Size back into the equation by forcing the assumption of homoskedasticity onto your estimation. The results are as follows:
c一ost
R2
= 
,(
,(
= 0.72, SER = 3, 682.02
Calculate the t-statistic on the Size coefficient and perform the hypothesis test that its coefficient is zero. Is this test reliable? Explain.
(h) What can you say about causation in the above relationship? Is it possible that Cost affects Reputation rather than the other way around?
2. Empirical exercise, to be solved using Stata. In this exercise you will investigate the relationship between housing prices and the physical characteristics of a home. On the course website you will find a data file hprice.csv (in comma dellimited format), collected from the real estate pages of the Boston Globe in 1990 (these are homes selling in the Boston, MA area). It contains data on the selling price (price) of the house (in $1000), the size (sqrft) of the house in square feet, the number of bedrooms (bdrms), the size of the lot (lotsize) in square feet, and a dummy variable (colonial) which is equal to 1 if the home was colonial style. Use these data to answer the following questions. In all your regressions, please use heteroskedasticity-robust standard errors and include an intercept term (i.e. β0 ). Make sure to include your Stata output with your homework!
(a) Run a regression of selling price (price) on the size of the home (sqrft) and the number of bedrooms (bdrms) and report your results.
(b) What is the estimated increase in price for a house with one more bedroom, holding square footage constant?
(c) What is the estimated increase in price for a house with an additional bedroom that is 140 square feet in size? Compare this to your result in part b).
(d) What percentage of the variation in price is explained by square footage and the number of bedrooms?
(e) The first house in the sample has sqrft = 2, 438 and bdrms = 4. Find the predicted selling price for this house from the OLS regression line.
(f) The actual selling price of the first house in the sample was $300,000 (so price = 300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?
(g) Suppose that instead of the regression described in part a), you ran a regression of price on sqrft (i.e. you left out bedrooms). Would you expect this regression to suffer from an omitted variables problem? If so, in what direction would you expect the coefficient on sqrft to be biased? Now run this regression and see if you were right.
(h) Now, suppose you included lotsize in the original regression. Will you have a problem with perfect multicollinearity? Why or why not? Run this regression (if you can) and interpret the coefficient on lotsize.
2023-05-02